tan ½a = γ/F
where γ is, numerically, the radius of the field sharp enough for the purpose in hand, and F the effective focal length of the ocular.
[19] There are binoculars on the market which are to outward appearance prism glasses, but which are really ordinary opera glasses mounted with intent to deceive, sometimes bearing a slight variation on the name of some well known maker.
[20] r the radius of the ring, is given by, r = (15/2)(t′-t) cos Dec., t′-t being the seconds taken for transit.
[21] (For full discussion of this instrument see Chandler, Mem. Amer. Acad. Arts & Sci. 1885, p. 158).
[22] For the principle of diffraction spectra see Baly, Spectroscopy; Kayser, Handbuch d. Specktroskoie or any of the larger textbooks of physics.
[23] The effect on the observed height of a prominence is h = h′ sin c/sin t, where h is the real height, h′ the apparent height, c the angle made by the grating face with the collimator, and t that with the telescope (Fig. 146).
[24] If A be the brightness of one object and B that of the other, α the reading of the index when one image disappears and β the reading when the two images are equal then A/B = tan²(α-β). There are four positions of the Nicol, 90° apart, for which equality can be established, and usually all are read and the mean taken. (H. A. II, 1.)
[25] For full description and method see H. A. Vol. 14, also Miss Furness’ admirable “Introduction to the Study of Variable Stars,” p. 122, et seq. Some modifications are described in H. A. Vol. 23. These direct comparison photometers give results subject to some annoying small corrections, but a vast amount of valuable work has been done with them in the Harvard Photometry.
[26] The general order of precision attained by astronomical photometers is shown in the discovery, photographically, by Hertzsprung in 1911, that Polaris, used as a standard magnitude for many years, is actually a variable. Its period is very near to four days, its photographic amplitude 0.17 and its visual amplitude about 0.1, i.e., a variation of ± 5 per cent in the light was submerged in the observational uncertainties, although once known it was traced out in the accumulated data without great difficulty.